Blind deconvolution for multidimensional images

Abstract

There are a number of technical situations where inversion of measured data involves blind deconvolution (i.e. the point spread function is unknown a priori) in three (or more) dimensions. We show that a unique solution exists for three-dimensional (3D) blind deconvolution for a particular sampling of the Fourier transform of a blurred image whose average density is less than the Nyquist density. This suggests that 3D blind deconvolution problems may be easier to solve than 2D problems. Experiments using an iterative blind deconvolution algorithm indicate that convergence is faster for the 3D case than for the 2D case, and that reducing the sampling density has a rather small effect on the quality of reconstructions. >